Exponential model representing the amount of Iodine-125 remaining in the tumor after t days is f(t) = 0.5 *[tex]e^{-0.0115t}[/tex] and number grams of Iodine-125 after 60 days is 0.2507 grams
Given:
A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.
The formula for exponential decay is f(t)=a*e^kt where a is the original amount of the substance, k is the decay rate and t is the time elapsed. You are given the decay rate of 1.15% or -0.0115. For this problem t is left as is since we are creating a function of time.
f(t) = 0.5 *[tex]e^{-0.0115t}[/tex]
After 60 days
= 0.5 * [tex]e^{-0.0115*60}[/tex]
= 0.5*e^-0.69
= 0.5*0.50157
f(t) = 0.2507 grams
Learn more about the exponential model here:
https://brainly.com/question/28596571
#SPJ4
Find the absolute value of the complex number.
2+i
Under any circumstances, the imaginary number i = √-1. We use i to represent the square root of a negative number because negative numbers cannot have square roots (ex: 2^2 = 4, -2^2 = 4).
So, we have a complex number 2 + i. The absolue value? Simple.
[tex]|2 + i|\\2 + |\sqrt{-1} |\\2 + \sqrt{1} \\2 + 1\\3[/tex]
If you need an explanation, look at it this way. The number cannot exist. Yet let's assume it did exist for a moment. What would be the absolute value of a negative square root if they could exist? Well, it would be the same as the square root of that number's opposite, it's positive counterpart!
So, what is the positive counterpart of -1? That would be 1. What's the square root of 1? 1! So, why don't we eliminate these steps? Instead of assuming √-1 can exist and then finding the absolute value of that, just skip those steps and instead take √1, or just 1.
So finally: |√-1| = 1
100 PONTS FOR ANSWERING 5-6 Q'S THANK YOU
11. Tell whether the sequence is arithmetic. If it is, what is the common difference?
19, 11, 3, negative 5 (1 point)
No
Yes; one-eighth
Yes; 8
Yes; negative 8
12. Grass seeds grow rapidly. A grass seed has grown to a 12 millimeter tall blade of grass. Tomorrow it will be 23 millimeters tall, the next day it will be 34 millimeters tall, and on the next day it will be 45 millimeters tall. Write a rule to represent the height of the blade of grass as an arithmetic sequence. How tall will the blade of grass be in 15 days? (1 point)
A(n) = 16 + (n – 1)11; 194 millimeters
A(n) = 12 + (n – 1)11; 166 millimeters
A(n) = 13n; 195 millimeters
A(n) = 12n; 180 millimeters
13. A magician charges $50.00 for a visit and an additional $7.50 for each hour he performs. The function rule C = 7.50h + 50.00 describes the relationship between the number of hours h and the total cost of the visit C. If the magician will only visit a maximum of 8 hours, what is a reasonable graph of the function rule? (1 point)
14. What is the graph of the function rule?
y = |3x| – 1 (1 point)
Answer:
Step-by-step explanation:
11 = D. Yes ; -8
12 = A(n) = 12+ (n-1) 11 ;166 milliliters
13 = The first plot graphed is located nearest 50 to resemble the initial charge.
The last plot graphed should be located at the top of the graph vertical to 8 - the maximum hours he'll work.
Therefore, the answer is C.
14 = you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point
In 2015, sarah spent $800 buying lunches. In 2017, she spent $550 buying lunches. What was the rate of change from 2015 to 2017?.
As per the Sarah buying pattern, the rate of change from 2015 to 2017 is $250
Rate of change
Rate of change refers the speed at which a variable changes over a specific period of time.
Given,
In 2015, sarah spent $800 buying lunches. In 2017, she spent $550 buying lunches.
Here we need to find the rate of change from 2015 to 2017.
While we looking into the given question, we have identified that,
Buying lunch cost for 2015 = $800
Buying lunch cost for 2017 = $550
Now, the rate of change from 2015 to 2017 is calculated by finding the difference between them,
So, rate of change is,
=> 800 - 550
=> 250
Therefore, the rate of change from 2015 to 2017 is $250
To know more about Rate of change here.
https://brainly.com/question/13103052
#SPJ1
Choose the expression that is equivalent to 1/5 x 3
Answer:
0.2
Step-by-step explanation:
1/5 is equvalent with 10/5=0.2
Shivani won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives
Shivani a bucket of fish to divide evenly among 3 dolphins. Each dolphin gets 6 fish.
Which equation can you use to find the number of fish f in the bucket before Shivani feeds
the dolphins?
Pls help ASAP
Answer:
Step-by-step explanation:
f/4 = 3
Determine whether the expression is a monomial. 1/2(c^3)(d^6)
A. Monomial
B. Not a monomial
Answer:
not a monomial
Step-by-step explanation:
monomial
Prefix mono- means 1 so, monomial means one term
This has more than one term so it’s not a monomial
Hopes this helps please mark brainliest
The mean of a normal distribution is 400 kilos. The standard deviation is 10 kilos. What is the probability of a weight between 420 kilos and the mean of 400
kilos?
****
0.1932
O 0.4772
0.4332
O0.5000
Second option is correct 0.04772.
The probability of a weight between 420 kilos and the mean of 400
kilos = 0.4772
Mean of a normal probability distribution is μ = 400 kilos
And standard deviation σ = 10 kilos
Let x be the variable in kilos.
X is between 400 kilos and 420 kilos
P( 400 < X < 420 ) = P ( 400 - μ < X - μ < 420 - μ)
= P ( (400-μ)/σ < (X-μ)/σ < (420-μ)/σ )
= P ( (400 - 400) /10 < Z < (420 - 400)/10 )
= P ( 0 < Z < 2 )
= 0.4777 from the table appendix B1.
The link for the appendix table B1 :
www.webassign.net%2Faswsbe13%2Fappendix-b.pdf&usg=AOvVaw3QlkaDTdGZ1Z01YZPYCL6h
The probability of a weight between 420 kilos and the mean of 400
kilos = 0.4772
To know more about probability here
https://brainly.com/question/112349
#SPJ1
Find a polynomial function with real coefficients that has the given zeros
-1, 8,3 - 21,
A polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
In the given question we have to find a polynomial function with real coefficient that has the given zeros -1, 8,3, -21.
The given zeros are -1, 8,3 - 21.
Let the variable is x.
So the factor from the given zeros are
(x-1), (x+8), (x+3), (x-21)
To find the polynomial we multiply the factors to each other.
=(x-1)(x+8)(x+3)(x-21)
We firstly multiply the factor with the pair of two using the distributive property.
={x(x-1)+8(x-1)}{x(x+3)-21(x+3)}
=(x^2-x+8x-8)(x^2+3x-21x+63)
Simplifying
=(x^2+7x-8)(x^2-18x+63)
=x^2(x^2+7x-8)-18x(x^2+7x-8)+63(x^2+7x-8)
=(x^4+7x^3-8x^2)-(18x^3+126x^2-144x)+(63x^2+441x-504)
=x^4+7x^3-8x^2-18x^3-126x^2+144x+63x^2+441x-504
=x^4−11x^3−197x^2−297x+504
Hence, a polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
To learn more about polynomial function from zeros link is here
brainly.com/question/17158670
#SPJ1
Find the value of x.
The value of x on the given sides of the rectangles is 4.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, The area of the shaded region is 39.
As the smaller rectangle is inside the whole larger rectangle,
∴The area of the smaller rectangle subtracted from the area of the whole larger rectangle is the area of the shaded region.
So, (2x - 1)(x + 3) - (x - 2)(x + 1) = 39.
2x² + 6x - x - 3 - x² - x + 2x + 2 = 39.
x² + 6x - 1 = 39.
x² + 6x - 40 = 0.
x² + 10x - 4x - 40 = 0.
x(x + 10) - 4(x + `10) = 0.
(x + 10)(x - 4) = 0.
(x + 10) = 0 Or (x - 4) = 0.
x = - 10 Or x = 4.
Now if we put x = - 10 the lengths will be negative which is inappropriate.
So, the value of x that satisfies is 4.
learn more about rectangles here :
https://brainly.com/question/15019502
#SPJ1
What is the slope of a line perpendicular to the line whose equation is x-2y=-8 Fully simplify your answer.
Answer:
[tex]-2[/tex]
Step-by-step explanation:
The perpendicular slope is the opposite of the reciprocal of the original slope. So, let's find the slope of this line! I will put it in slope-intercept form (y = )
[tex]x-2y=-8\\-2y=-8-x\\y=4+\frac{1}{2} x\\y=\frac{1}{2} x+4[/tex]
Here, I see that the slope of the line is [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2. The opposite of 2 is [tex]-2[/tex]. The slope of the perpendicular line is [tex]-2[/tex]!
A & B = (A + B) x A + (A - B) divided by B. find the value of 4 & - 2.
Answer:
-7
Step-by-step explanation:
A= 4
B= -2
((4-2) × 4 + (4+2))/-2
14/-2
-7
Determine the relationship between the X and Y values write an equation
1 -2
2 -4
3 -6
The equation is, y = x-2
The table showing the values of x and y is:
x 1 2 3 4
y -1 0 1 2
From the question, we have
y increases by 1 unit with 1 unit increase in x.
The equation is, y = x-2
Subtraction:
Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.
To learn more about subtraction visit: https://brainly.com/question/2346316
#SPJ9
Solve the equation: 12x+18=16x
Answer:
Step-by-step explanation:
answer is: x=9/2
Which equation illustrates the identity property of multiplication? (x yi) × z = (xz yzi) (x yi) × 0 = 0 (x yi) × (z wi) = (z wi) × (x yi) (x yi) × 1 = (x yi)
The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
In the question ,
Four equations are given , we need to find the equation that represents the identity property of multiplication .
we know that the identity property of multiplication states that the product of any number and 1 is the same given number .
For Example : the product of a number 'a' and 1 is = a , that is a×1 = a .
So , by the applying the definition of Identity property of multiplication we get that the equation that models the identity property is
(a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi)
Therefore , The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
The given question is incomplete , the complete question is
Which equation illustrates the identity property of multiplication?
(a) (a + bi) × c = (ac + bci)
(b) (a + bi) × 0 = 0
(c) (a + bi) × (c + di) = (c + di) × (a + bi)
(d) (a + bi) × 1 = (a + bi)
Learn more about Identity Property here
https://brainly.com/question/1407048
#SPJ4
Evaluate 4y - 5x + 10m
y=2 x=3 m=5
Answer:
43
Step-by-step explanation:
4(2)-5(3)+10(5)
8-15+50
-7+50
43
hopes this helps please mark brainliest
Answer:
17/54,x=3 m=5
Step-by-step explanation:
QUICK!! EMERGENCY!! PLEASE HELP ME!!
As shown in the graph, Jane has a car payment of $200 a month. Her loan amount is $3,000. Assume there is no interest.
A. What is the slope of the line?
What does this slope in this situation mean?
B. What is the y-intercept of the line?
What does the y-intercept mean in this situation?
C. How many months will it take Jane to pay off the loan?
Show your work.
Answer:
A ) What is the slope of the line? What does this slope in this situation mean?
The equation of the line is y = -200x +3000 so the slope of the line would be -200x.
This means that as x ( Month ) increases, y ( Loan ) decreases.
B ) What is the y-intercept of the line? What does the y-intercept mean in this situation?
As stated above the equation of the line is y = -200x +3000 so the y-intercept would be +3000.
In this case the y-intercept represents the cost of the loan before Jane's first payment.
C ) How many months will it take Jane to pay off the loan? Show your work.
It will take 15 months to pay off Jane's car loan.
On the graph we can see when x ( month ) equals fifteen, y ( loan ) equals zero. This means that it will take fifteen months for Jane to pay off the loan.
We can check this by putting it into our equation...
y = -200( 15 ) +3000 = 0
Hope this helps! :)
1
Based on the triangle shown, what is the approximate value of COS(20)?
Use exact fractions. To receive credit for this question, you must show your work.
SHOW WORKKK
Answer:
?
Step-by-step explanation:
its a litter hard too see can you get it closer??
7/2x + 1/2x = 7 + 9/2x
Answer: x=-14
Step-by-step explanation:
A bike path is 12.5 miles. Dominic is 70% of the way to the end. How far is Dominic on the path? HELPPP PLEASE :
Answer:
The percentage of the distance Dominic is on the path is his distance
travelled as a fraction of the total distance when equivalent to 100.
The distance he has travelled on the path is 8.75 miles.
Reasons:
The given parameter are;
Length of Dominic's path = 12.5 miles
The length of the way Dominic is to
Step-by-step explanation:
During the past five months, Elle
spent $3.25 on candy, $12.09 on
cupcakes, and $9.88 on chips. ABOUT
how much did Elle spend?
There are two more quarters than dimes and as many nickles as quarters and dimes together. The total amount of money is 3.75. How many quarters, dimes and nickles are there?
Answer: 9 quarters, 7 dimes, & 16 nickels
Step-by-step explanation:
We set number of dimes as d:
Number of quarters: d + 2Number of nickels: d + 2 + d = 2d + 2So, set up the equation to solve:
[tex]0.10d+0.25(d+2)+0.05(2d+2)=3.75\\\\0.10d+0.25d+0.5+0.1d+0.1=3.75\\\\0.45d=3.75-0.5-0.1=3.15\\\\d=7[/tex]
So now that we know there're seven dimes, we can plug them in our initial equations to find the number of quarters and nickels:
Number of quarters: d + 2 = 7 + 2 = 9Number of nickels: d + 2 + d = 2d + 2 = 2(7) + 2 = 16Use the quadratic formula to solve for x.
8x²-8x-1=0
Answer:
in the picture
Step-by-step explanation:
Hope this helped! Solve your problem: Use the quadratic formula to solve for x.
8x²-8x-1=0
Between 10 P.M. and 7:54 A.M., the water level in a swimming pool decreased by 11/40 . Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Answer:
It approximately dropped 0.027777 per hour.
Step-by-step explanation:
First, we calculate the decrease.
Decrease = 11/40 = 0.275
Then, we calculate the time interval.
From 10 pm to 7:54 hours will be 9.54 hours
Time interval= (9 + 54/60) hours
Time interval=9.9 hours
Finally, we calculate how much it dropped each hour
0.275/9.9 ≈ 0.027777
So it approximately dropped 0.027777 per hour.
Answer:
7:54 A.M to 10 P.M is = 14 hrs and 6 mins
60 mins = 1 hour
therefore 6 mins = 0.1 hour
14 hrs plus 0.1 hrs = 14.1 hours
if 14.1 hrs = 11/40
1 HR = x
cross multiply
14.1x = 11/40
divide both sides by 14.1
14.1x / 14.1 = 11/40 / 14.1
X = 11/564 or 0.0195 times every hourSpecial right triangles
In the special right triangle, x has a value of √3/2
Special Right TriangleA special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.
To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.
Using Pythagoras theorem;
[tex](\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }[/tex]
The value of x in the triangle is √3/2
Learn more special right triangle here;
https://brainly.com/question/2217700
#SPJ1
123.05 to the nearest cent
Answer:
123.00
Step-by-step explanation:
forty percent of students at sbcc have brought their own personal computers to campus. a random sample of 120 entering freshmen was taken. what is the standard error of the sample proportion bringing their own personal computers to campus? round your answer to 3 decimal places.
The standard error of the sample proportion bringing their own personal computers to campus is 0.045
The standard error of a sample proportion is calculated as:
[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]
with p=0.4 and n=120:
[tex]SE=\sqrt{\frac{0.4(1-0.4)} {120}}[/tex]
[tex]SE=\sqrt{0.002}[/tex]
[tex]SE=0.045[/tex]
The standard error of the sample proportion of students bringing their own computer is 0.045.
To learn more standard errors about, visit:
https://brainly.com/question/13179711
#SPJ4
Nina has some nickels and 9 pennies in her pocket. Her friend, Maurice, has twice as many nickels as Nina. Together, these coins are worth 84¢. How many nickels does Nina have? Show all of your work and label your answers
Answer:
x = 5
Step-by-step explanation:
Let's say
x = #s of nickels Nina has (we are going to try to get X)
y = # of nickels Maurice has
5x + 9 < The amount Nina has
y = 2x < Amount that Maurice has
Add them both to the total, 84
5x + 9 + 5y = 84
Transfer the 9 to the other side
5x + 5y = 75
Substitute y with it's value
5x + 5(2x) = 75
5x + 10x = 75
15x = 75
Divide
x = 5
what is 100x100x200x1x2000x10000,000x40000x1000002x0000003xxxxxxxxxxxx000000
Answer:16.e+6.18
Step-by-step explanation:
Review for Features of Functions Assessment
Suppose that the function f(x) = 20 + 5.5x represents the cost of making x t-shirts.
a. What is f(12)?
b. What does your answer to part a mean in context?
the bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially
The initial size of the bacteria culture is 33
The count of the bacteria after 10 days = 200
The count of bacteria after 20 days = 1200
The difference in time = 20 - 10
= 10 days
Then the exponential growth equation will be
1200 = 200×[tex]e^{10k}[/tex]
[tex]e^{10k}[/tex] = 1200 / 200
Divide the terms
[tex]e^{10k}[/tex] = 6
10k = ln(6)
10k = 1.79
k = 1.79 / 10
Divide the terms
k = 0.179
Use the same equation to find the initial size of the bacteria culture
200 = x × [tex]e^{10(0.179)}[/tex]
x = 200 / [tex]e^{10(0.179)}[/tex]
x = 200 / 5.99
Divide the terms
x = 33.38
x ≈ 33
Hence, the initial size of the bacteria culture is 33
The complete question is:
The bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially. Find the initial size of the bacteria culture
Learn more about exponential growth here
brainly.com/question/11487261
#SPJ4